$\frac{1}{2}$ : 3 + $\frac{1}{3}$ : 4 + $\frac{1}{4}$ : 5 + …+ $\frac{1}{2019}$ : 2020

0 bình luận về “$\frac{1}{2}$ : 3 + $\frac{1}{3}$ : 4 + $\frac{1}{4}$ : 5 + …+ $\frac{1}{2019}$ : 2020”

1. Đáp án:  `1009/2020`

    

   Giải thích các bước giải:

    `1/2 :  3 + 1/3 :  4 + 1/4 : 5 + … + 1/2019 : 2020`

   `= 1/2 X 1/3 + 1/3 X 1/4 + 1/4 X 1/5 + … + 1/2019 X 1/2020`

   `= 1/(2 X 3) + 1/(3 X 4) + 1/(4 X 5) + … + 1/(2019 X 2020)`

   `= 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/2019 – 1/2020`

   `= 1/2 – 1/2020`

   `= 1010/2020 – 1/2020`

   `= 1009/2020`

    

   Trả lời

2. `1/2:3+1/3:4+1/4:5+…+1/2019:2020`

   `=1/2×1/3+1/3×1/4+1/4×1/5+…+1/2019×1/2020`

   `=1/{2×3}+1/{3×4}+1/{4×5}+…+1/{2019×2020}`

   `=1/2-1/3+1/3-1/4+1/4-1/5+…+1/2019-1/2020`

   `=1/2-1/2020`

   `=1010/2020-1/2020`

   `=1009/2020`

    

   Trả lời